Conditions for ANOVA

Inference for Numerical Data in R

Mine Cetinkaya-Rundel

Associate Professor of the Practice, Duke University

Conditions for ANOVA

  • Independence:
    • within groups: sampled observations must be independent
    • between groups: the groups must be independent of each other (non-paired)
  • Approximate normality: distribution of the response variable should be nearly normal within each group
  • Equal variance: groups should have roughly equal variability
Inference for Numerical Data in R

Independence

  • Within groups: Sampled observations must be independent of each other

    • Random sample / assignment
    • Each $n_j$ less than 10% of respective population always important, but sometimes difficult to check

  • Between groups: Groups must be independent of each other

    • Carefully consider whether the groups may be dependent
Inference for Numerical Data in R

Approximately normal

  • Distribution of response variable within each group should be approximately normal
  • Especially important when sample sizes are small
  • Check with visuals
Inference for Numerical Data in R

Constant variance

  • Variability should be consistent across groups (homoscedasticity)
  • Especially important when sample sizes differ between groups
Inference for Numerical Data in R

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Inference for Numerical Data in R

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